The Duchess of Cambridge has been admitted to the private Lindo wing at St Mary's hospital in London, in preparation for the birth of her first child.

In a brief statement released at 7.30am, Kensington Palace said: "Her Royal Highness the Duchess of Cambridge has been admitted this morning to St Mary's hospital, Paddington, London, in the early stages of labour.

"The duchess travelled by car from Kensington Palace to the Lindo wing at St Mary's hospital with the Duke of Cambridge."

The duchess arrived shortly before 6am. The couple travelled from the palace without a police escort, a spokesman said, adding: "Things are progressing as normal".

Royal aides have previously said that the duchess was planning a natural birth and the fact that she was in the early stages of labour supported this.

Members of the media have been camped outside St Mary's hospital for weeks. Photograph: Andy Rain/EPA

There was a strong police presence outside the hospital, and two officers guarded the entrance to the private wing.

The couple's private secretaries, Miguel Head and Rebecca Deacon, and two press officers are at the hospital.

A spokesman for Imperial College Healthcare NHS trust, which runs St Mary's hospital, said: "During her stay at the hospital, the Duchess is being cared for by an expert team of consultants and midwives.

"It goes without saying that the whole trust wishes her well and we are exceptionally proud that the Duke and Duchess of Cambridge have chosen to have their baby here."

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Barriers have been erected outside the hospital in anticipation of crowds gathering to celebrate the royal addition, who will be third in line to the throne.

Media pens have been in place outside the hospital since 1 July for the scores of international journalists covering the birth.

The first the world will know of the birth is when a royal aide leaves the main entrance of the Lindo wing bearing a typed medical bulletin signed by doctors at the birth. The aide will take the bulletin to Buckingham Palace by car with police outriders.

The announcement of the gender and other details of the baby will be made by the age-old custom of placing a proclamation on a dark wooden frame on an ornate easel behind the railings on Buckingham Palace's forecourt. No such details will be given until the Queen and other members of the couple's families have been informed.

The brief bulletin, on palace-headed foolscap paper, usually confirms the sex of the baby and the weight, but gives few other details. The easel will be the same one used to announce William's birth in 1982.

If it is a girl, the child will make history, becoming the first female firstborn of a future monarch to take precedence over a younger brother. In October 2011, David Cameron announced that the 16 Commonwealth countries where the Queen is head of state had agreed to give future female royals the same rights of succession as their brothers.

The succession to the crown bill cleared the House of Lords in April after being fast-tracked through both houses of parliament in three months and became law on 25 April. It will come into force once it is approved by the other Commonwealth countries who have the Queen as head of state.

The newest royal will be styled HRH Prince/Princess [name] of Cambridge. The Queen stepped in to ensure that her great-grandchild had a title befitting a future monarch. Under past rules only a first-born boy of the Duke and Duchess of Cambridge would automatically have become a prince, with a daughter being styled lady instead of princess and not known as Her Royal Highness.

The Queen issued Letters Patent under the Great Seal of the Realm when Kate was about three months pregnant. The decree declared: "All the children of the eldest son of the Prince of Wales should have and enjoy the style, title and attribute of royal highness with the titular dignity of prince or princess prefixed to their Christian names or with such other titles of honour."

The duchess is making use of exclusive facilities at the hospital, which offers bespoke care packages. William and his brother, Prince Harry, were born in the same wing. It was refurbished last year, and is described as having offered "leading private obstetric and neonatal care for 60 years". It has private en suite rooms designed to provide "comfort and privacy" and deluxe rooms and suites.

A normal delivery package, including a one-night stay, costs £4,965, with an extra night in a deluxe room costing £1,050 plus consultant's fees, which can be as much as £6,000 depending on the care required. A suite of two rooms, with consultant fees, would be about £14,465.

The wing also has the benefit of being based in an NHS hospital, should any complications arise. Facilities include the Winnicott baby unit, which is at the forefront of specialist care for premature and critically ill newborns.

On Monday, it was business as usual for other members of the royal family. Prince Charles, about to become a grandfather for the first time, is in York on a visit to the National Railway Museum. He will also visit York Minster. Asked if he had heard any news, he replied "absolutely nothing". Prince Harry is at RAF Wattisham with his Apache squadron.

The Queen was at Windsor Castle, and had no royal engagements on Monday. She is due to travel to Balmoral, her Scottish estate, for her annual summer holiday on Friday. Last week, she joked that she wished the royal baby would hurry up and arrive before she went away.

David Cameron said of the news: "Best wishes to them. A very exciting occasion and the whole country is excited with them." Speaking later on BBC Radio 4's Woman's Hour, he said he had been "pretty involved" in the birth of his own children.

"I can't claim any role in this one, I'm afraid, except one small thing – well, it's a big thing actually – which is to get all of the heads of the realms over which our Queen is queen, to agree that whatever the sex of the baby that Will and Kate have, if it's a girl, it will be our queen."

The royal birth was trending on Twitter. The archbishop of Canterbury, Justin Welby, tweeted: "My thoughts and prayers are with Kate and the whole family on this enormously special day."

Broadcaster Piers Morgan tweeted: "Keep Calm … and Carry On #Kate" and added: "My money's on an Australian cricket birth – all out by tea." Labour's former deputy prime minister John Prescott joked: "Great to hear the Duchess of Cambridge has gone into labour. Is she an affiliated member?" Meanwhile, wellwishers were beginning to gather outside Buckingham Palace.

The Duke and Duchess of Cambridge leaving King Edward VII hospital in December. The couple have opted for a natural birth. Photograph: Leon Neal/AFP/Getty Leon Neal/AFP/Getty Images

The couple were forced to announce the pregnancy earlier than they would have wished after the duchess was admitted to the King Edward VII hospital suffering from hyperemesis gravidarum, or acute morning sickness.

The baby will be the Queen's third great-grandchild, and could one day be head of the armed forces, supreme governor of the Church of England, and head of state of 16 countries. He or she will also be head of the Commonwealth.

Prince Harry will move from third to fourth in line to the throne, while the Duke of York will move to fifth position and his daughters, Princesses Beatrice and Eugenie, to sixth and seventh place.

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